Jon Snow is quite popular. People like to be reincarnated as him because he has a lot of potential for growth and a mysterious backstory. They can use their new knowledge to perhaps avoid some of his tragedies and rise to power more quickly.
It would be amazing. Imagine being reincarnated as a noble or a powerful sorcerer in the world of Game of Thrones fanfiction. You could use your knowledge of the original series to gain an edge. Maybe you'd befriend the Starks and help them in their battles. Or perhaps you'd explore the unknown parts of Essos that were only hinted at in the show.
Jon Snow is quite popular. Given his complex backstory and his role in the original series, seeing him reincarnated in different scenarios is fascinating. People like to explore what would happen if he had a second chance at life with different knowledge or abilities. Daenerys Targaryen is also a common choice. Her journey as the 'Mother of Dragons' makes her a prime candidate for reincarnation stories, perhaps to correct the mistakes she made in her first life.
Some fanfictions play with the concept of reincarnation and magic. A character might be reincarnated with some sort of magical ability they didn't have before. This could be related to the old gods or the new. For instance, a character reincarnated with the ability to communicate with the weirwoods in a more powerful way than before. This could give them an edge in the game of thrones, as they could gain knowledge and wisdom from the ancient trees that others can't access.
Another plotline might involve reincarnation as a wildling. The character then tries to unite the wildlings in a more organized way, using their knowledge of military tactics from the modern world. They could form alliances with some of the northern houses, changing the whole dynamic of the conflict between the Night's Watch and the wildlings.
One should quickly learn the political landscape. Know which houses are allied and which are enemies. For example, staying away from the Lannisters if you're not on their good side. Also, learn some basic combat skills as self - defense is crucial in Westeros.
Cersei could be the most interesting in a sense. If she were reincarnated, she could either double down on her power - hungry ways or completely change. Maybe she could learn from her past mistakes and become a more benevolent ruler. Or she could use her reincarnation as a way to exact revenge on those who opposed her in her previous life in more devious and calculated ways.
One idea could be reincarnating as a minor character, like a servant in King's Landing. You could use your modern knowledge to avoid the chaos of the city and slowly rise in power by befriending key players. Maybe you know of some herbal remedies that could save a noble from a deadly illness and gain their favor.
One idea could be a character reincarnated as a different species, like a dragon. They could then use their new form to influence the power struggles in Westeros. Another could be a reincarnated character remembering key events from the original series and trying to prevent certain tragedies from occurring. For example, if Ned Stark was reincarnated, he might be more cautious and avoid getting caught in the political traps that led to his downfall.
Reincarnating as Tyrion Lannister would be really interesting. He's already a complex character with a sharp mind. As someone reincarnated, you could use your modern ideas to enhance his political acumen even more. You could also try to change his relationship with his family for the better, or at least make his life less miserable while still being the clever dwarf everyone fears and respects in the political arena.